We compute complete leading logarithms in Φ4 theory with the help of Connes and Kreimer RG equations. These equations are defined in the Lie algebra dual to the Hopf algebra of graphs. The results are compared with calculations in parquet approximation. An interpretation of the new RG equations is discussed.

The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of union-soft sets is introduced, and its application to BCK/BCI-algebras is considered. The notions of union-soft algebras, union-soft (commutative) ideals and closed union-soft ideals are int...

We studied equilibrium conformations of trivial-, 31-knot, and 51-knot ring polymers with finite chain length at their θ-conditions using a Monte Carlo simulation. The polymer chains treated in this study were composed of beads and bonds on a face-centered-cubic lattice respecting the excluded volume. The Flory's critical exponent ν in Rg ~ N(ν) relationship was obtained from the dependence of ...

In this paper, we define a soft generalized ?-closed set, which is generalization of both the set and closed set. We show that classes sets coincide in anti-locally countable topological spaces. Additionally, locally spaces, every Furthermore, prove space (X,??,A). addition to these, determine behavior relative unions, intersections, subspaces, generated topologies. investigate images inverse u...

Several notions on soft topology are studied and their basic properties investigated by using the concept of pre open sets closure operator which derived from basics set theory established Molodtsov [1]. In this paper we introduce some separation axioms called Soft R0 R1 in topological spaces defined over an initial universe with a fixed parameters. Many characterizations these have been demons...

In this paper, we introduce the concept of soft supra strongly semi∗ generalized closed sets (soft supra strongly semi∗ g-closed for short) in a supra soft topological space (X,μ,E) and study their properties in detail. The relationship between soft supra strongly semi∗ generalized closed sets and other existing soft sets have been investigated. It has been pointed out in this paper that many o...